Thermal Casimir effect at fluid interfaces: Fluctuation-induced forces between anisotropic colloids

We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. Within a coarse-grained picture, the properties of fluid interfaces are very well described by an effective capillary wave Hamiltonian which governs both the equilibrium interface configuration and the thermal fluctuations (capillary waves) around this equilibrium (or mean-field) position. As postulated by the Goldstone theorem the capillary waves are long-range correlated. The interface breaks the continuous translational symmetry of the system, and in the limit of vanishing external fields - like gravity - it has to be accompanied by easily excitable long wavelength (Goldstone) modes – precisely the capillary waves. In this system the restriction of the long-ranged interface fluctuations by particles gives rise to fluctuation-induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example for the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuating multipole moments of an auxiliary charge density-like field defined on the area enclosed by the contact lines. These fluctuations are coupled to fluctuations of multipole moments of the contact line position (due to the possible position and orientational fluctuations of the colloids). We obtain explicit expressions for the behavior of the Casimir interaction at large distances for arbitrary ellipsoid aspect ratios. If colloid fluctuations are suppressed, the Casimir interaction at large distances is isotropic, attractive and long ranged (double-logarithmic in the distance). If, however, colloid fluctuations are included, the Casimir interaction at large distances changes to a power law in the inverse distance and becomes anisotropic. The leading power is 4 if only vertical fluctuations of the colloid center are allowed, and it becomes 8 if also orientational fluctuations are included.

Transverse trapping forces of focused Gaussian beam on ellipsoidal particles

A modified T-matrix method is presented to compute the scattered fields of various realistically shaped particles; then the radiation forces on the particles can be calculated via the Maxwell stress tenser integral. Numerical results of transverse trapping efficiencies of a focused Gaussian beam on ellipsoidal and spherical particles with the same volume are compared, which show that the shape and orientation of particles affect the maximal transverse trapping force and the displacement corresponding to the maximum. The effect of the polarization direction of the incident beam on the transverse trapping forces is also revealed. (c) 2007 Optical Society of America.

Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

Action of the gravitational field on the dynamical Casimir effect

In this paper, we analyze the action of the gravitational field on the dynamical Casimir effect. We consider a massless scalar field confined in a cuboid cavity placed in a gravitational field described by a static and diagonal metric. With one of the plane mirrors of the cavity allowed to move, we compute the average number of particles created inside the cavity by means of the Bogoliubov coefficients computed through perturbative expansions. We apply our result to the case of an oscillatory motion of the mirror, assuming a weak gravitational field described by the Schwarzschild metric. The regime of parametric amplification is analyzed in detail, demonstrating that our computed result for the mean number of particles created agrees with specific associated cases in the literature. Our results, obtained in the framework of the perturbation theory, are restricted, under resonant conditions, to a short-time limit.

Casimir effect with quantized charged spinor matter in background magnetic field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged spinor matter field confined between two parallel neutral plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the Dirac Hamiltonian operator be self-adjoint. It is shown that, in the case of a sufficiently strong magnetic field and a sufficiently large separation of the plates, the generalized Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates. The detection of this effect seems to be feasible in the foreseeable future.

Stochastic Modeling of Reversible Biochemical Reaction-Diffusion Systems and High-Resolution Shock-Capturing Methods for Fluid Interfaces

Thesis (Ph.D.)--University of Washington, 2016-08

Eigenstrain boundary integral equations with local Eshelby matrix for stress analysis of ellipsoidal particles

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.

Growth, self-assembly and dynamics of nano-scale films at fluid interfaces

Ultrathin films at fluid interfaces are important not only from a fundamental point of view as 2D complex fluids but have also become increasingly relevant in the development of novel functional materials. There has been an explosion in the synthesis work in this area over the last decade, giving rise to many exotic nanostructures at fluid interfaces. However, the factors controlling particle nucleation, growth and self-assembly at interfaces are poorly understood on a quantitative level. We will outline some of the recent attempts in this direction. Some of the selected investigations examining the macroscopic mechanical properties of molecular and particulate films at fluid interfaces will be reviewed. We conclude with a discussion of the electronic properties of these films that have potential technological and biological applications.

Casimir Effect on the Pull-in Parameters of Nanometer Switches

Casimir effect on the critical pull-in gap and pull-in voltage of nanoelectromechanical switches is studied. An approximate analytical expression of the critical pull-in gap with Casimir force is presented by the perturbation theory. The corresponding pull-in parameters are computed numerically, from which one can notice the nonlinear effect of Casimir force on the pull-in parameters. The detachment length has been presented, which increases with increasing thickness of the beam.

Photon Production from the Vacuum Close to the Superradiant Transition: Linking the Dynamical Casimir Effect to the Kibble-Zurek Mechanism

The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuations of an electromagnetic field. The verification of such an effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way to an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of the DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.

The Casimir effect in the presence of compactified universal extra dimensions

The Casimir force in a system consisting of two parallel conducting plates in the presence of compactified universal extra dimensions (UXD) is analyzed. The Casimir force with UXDs differs from the force obtained without extra dimensions. A new power law for the Casimir force is derived. By comparison to experimental data the size R of the universal extra dimensions can be restricted to R⩽10 nm for one extra dimension.

Number of particle creation and decoherence in the nonideal dynamical Casimir effect at finite temperature

In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary, under the only restriction of small velocities. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of a slow moving boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. Since our results were obtained in the framework of the perturbation theory, they are restricted, under resonant conditions, to a short-time approximation. (C) 2009 Elsevier Inc. All rights reserved.

Casimir effect for the scalar field under Robin boundary conditions: a functional integral approach

In this work we show how to define the action of a scalar field such that the Robin boundary condition is implemented dynamically, i.e. as a consequence of the stationary action principle. We discuss the quantization of that system via functional integration. Using this formalism, we derive an expression for the Casimir energy of a massless scalar field under Robin boundary conditions on a pair of parallel plates, characterized by constants c(1) and c(2). Some special cases are discussed; in particular, we show that for some values of cl and c(2) the Casimir energy as a function of the distance between the plates presents a minimum. We also discuss the renormalization at one-loop order of the two-point Green function in the philambda(4) theory subject to the Robin boundary condition on a plate.

Dynamical Casimir effect and the structure of vacuum in quantum field theory

Some of the most interesting phenomena that arise from the developments of the modern physics are surely vacuum fluctuations. They appear in different branches of physics, such as Quantum Field Theory, Cosmology, Condensed Matter Physics, Atomic and Molecular Physics, and also in Mathematical Physics. One of the most important of these vacuum fluctuations, sometimes called "zero-point energy", as well as one of the easiest quantum effect to detect, is the so-called Casimir effect. The purposes of this thesis are: - To propose a simple retarded approach for dynamical Casimir effect, thus a description of this vacuum effect when we have moving boundaries. - To describe the behaviour of the force acting on a boundary, due to its self-interaction with the vacuum.

Influence of quantized massive matter fields on the Casimir effect

Charged massive matter fields of spin-0 and spin- 1/2 are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed. Read More: http://www.worldscientific.com/doi/10.1142/S0217732315500996